# Is this correct? Casimir Effect

• I
• raracon
In summary, Maxwell's equations allow for field modes of arbitrarily large frequency both between and outside of two perfectly conducting plates. This results in an infinite zero-point field energy when the plates are separated by a finite distance, as well as when they are infinitely far apart. However, the difference in zero-point energy for these two cases is finite and can be described by the formula F = −πhc/480d^4 per unit area, where d represents the separation between the plates. This formula is derived based on the quantization of excitations by plane boundary conditions, which results in a lower vacuum energy between the plates compared to outside of them.
raracon
TL;DR Summary
Quick fact check
"In the example of Fig. 1, Maxwell’s equations allow field modes of arbitrarily large frequency both between the plates and outside them, and therefore the zero-point field energy is infinite when the plates are separated by a finite distance d as well as when they are infinitely far apart. However, the difference in zero-point energy for the two cases is finite, and its dependence on the plate separation d implies a force F = −πhc/480d^4 per unit area."

Fig 1:

Read this in a book about the Casimir Effect. Now my question is if it is correct to say that between the two perfectly conducting plates there can be modes with any frequency? I've read in other books that the frequency is limited by the separation between the plates.

And my other question is how does one explain F = −πhc/480d^4 ?

A Wiki article https://en.wikipedia.org/wiki/Casimir_effect shows formula, the excitation is quantized by plane boundary condition so lower vacuum energy than outside take place between the plates. The formula of F is also derived there.

## 1. What is the Casimir Effect?

The Casimir Effect is a physical phenomenon in which two parallel, uncharged plates placed in a vacuum experience an attractive force due to the fluctuations in the quantum vacuum.

## 2. How was the Casimir Effect discovered?

The Casimir Effect was first proposed by Dutch physicist Hendrik Casimir in 1948. He theorized that the energy of the vacuum between two plates would be different than the energy outside of the plates, resulting in a measurable force between them.

## 3. What is the significance of the Casimir Effect?

The Casimir Effect has significant implications in the field of quantum mechanics and has been experimentally confirmed multiple times. It also has potential applications in nanotechnology and the development of new energy sources.

## 4. Can the Casimir Effect be observed in everyday life?

No, the Casimir Effect is a very small force that is only noticeable on a microscopic scale. It is only observed in highly controlled laboratory conditions.

## 5. What are the current theories about the cause of the Casimir Effect?

The exact cause of the Casimir Effect is still a topic of debate among scientists. Some theories suggest that it is due to the interaction of virtual particles in the vacuum, while others propose that it is a result of the curvature of space-time caused by the plates.

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